Foye scored 18 points and Utah used a 17-2 run midway through the second quarter to build a halftime 58-48 lead.
The Jazz, who have lost five of their last seven, were trying to snap the Clippers' 15-game winning streak.
L.A. made five of its first seven shots and to take a 12-7 lead. It was 18-14 when Willie Green hit a three-pointer, triggering an 11-6 run.
Foye kept the Jazz in the game with 13 points in the first quarter, which ended with the Clippers owning a 29-21 lead.
Utah trailed, 34-29, before Enes Kanter's monstrous rebound dunk. He ignited the crowd and began the Jazz's 17-2 run, which carried them to a 46-36 lead.
Gordon Hayward scored 10 straight points in one stretch, including a free throw after a technical foul on Blake Griffin.
In the third quarter, the Jazz converted eight of their first 10 possessions during a 16-7 run. They built a 74-55 lead with 8:09 left.
It was 76-59 when Utah's defense disappeared. L.A. scored 12 straight points and finished the quarter by converting 12 of its final 13 possessions.
The Clippers trailed 88-84 heading into the fourth quarter. They tied the game 90-90 on Caron Butler's four-point play with 9:09 remaining.